I occasionally clean Swing related questions (from 01/jan/2011) on SO, and I want to get the Archaeologist Badge for that.

My question is if edits (to the posts that were inactive for 6 months and more) are recorded separately for the Copy Editor badge and the Archaeologist badge, or do I have to wait a few months for Copy Editor, then start to clean up the Swing posts

Badges exist to encourage behaviors that make the site/network/Internet a better place. Gold ones, especially, are nice to have, but you probably shouldn't wait to make the Internet better just to earn one.